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| In this definition, x is not necessarily a real [[number]], but can in general be a member of any [[vector]] [[space]]. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics. | | In this definition, x is not necessarily a real [[number]], but can in general be a member of any [[vector]] [[space]]. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics. |
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− | The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a [http://en.wikipedia.org/wiki/Differential_operator differential operator]], and many constructed from it, such as [http://en.wikipedia.org/wiki/Del del] and the [http://en.wikipedia.org/wiki/Laplacian Laplacian]. When a [http://en.wikipedia.org/wiki/Differential_equation differential equation] can be expressed in linear form, it is particularly easy to solve by breaking the [[equation]] up into smaller pieces, solving each of those pieces, and adding the solutions up. | + | The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a [https://en.wikipedia.org/wiki/Differential_operator differential operator]], and many constructed from it, such as [https://en.wikipedia.org/wiki/Del del] and the [https://en.wikipedia.org/wiki/Laplacian Laplacian]. When a [https://en.wikipedia.org/wiki/Differential_equation differential equation] can be expressed in linear form, it is particularly easy to solve by breaking the [[equation]] up into smaller pieces, solving each of those pieces, and adding the solutions up. |
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− | [http://en.wikipedia.org/wiki/Linear_algebra Linear algebra] is the branch of [[mathematics]] concerned with the [[study]] of [[vectors]], vector spaces (also called linear spaces), linear transformations (also called linear maps), and [[systems]] of linear equations. | + | [https://en.wikipedia.org/wiki/Linear_algebra Linear algebra] is the branch of [[mathematics]] concerned with the [[study]] of [[vectors]], vector spaces (also called linear spaces), linear transformations (also called linear maps), and [[systems]] of linear equations. |
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− | [http://en.wikipedia.org/wiki/Nonlinear Nonlinear equations] and [[functions]] are of interest to [[physicists]] and mathematicians because they can be used to represent many natural [[phenomena]], including [[chaos]].[http://en.wikipedia.org/wiki/Linear] | + | [https://en.wikipedia.org/wiki/Nonlinear Nonlinear equations] and [[functions]] are of interest to [[physicists]] and mathematicians because they can be used to represent many natural [[phenomena]], including [[chaos]].[https://en.wikipedia.org/wiki/Linear] |
| ==References== | | ==References== |
| 1. Heinrich Wölfflin, Principles of Art History: the Problem of the Development of Style in Later Art, M. D. Hottinger (trans.), Mineola, N.Y.: Dover (1950): pp. 18-72. | | 1. Heinrich Wölfflin, Principles of Art History: the Problem of the Development of Style in Later Art, M. D. Hottinger (trans.), Mineola, N.Y.: Dover (1950): pp. 18-72. |